Milan have endured a torrid recent run of form, tumbling out of the UEFA Champions League and losing their last four in all competitions before the visit to the Stadio Olimpico.
But their luck seemed to be changing when, in the space of a few minutes towards the end of the first period, Lazio's Diego Novaretti had a goal disallowed for offside and Kaka swung in a left-wing cross that went in via a deflection off the unfortunate Abdoulay Konko.
Keisuke Honda missed a gilt-edged chance to double their advantage moments before the break when he headed over Kaka's wonderful free-kick.
And that proved to be costly as Alvaro Gonzalez levelled with a bullet header.
Mario Balotelli struck a post late on after coming off the bench, but Seedorf declared himself 'satisfied' with the point.
He told Sky Sport Italia: "They showed that they are a compact group who want to go forward. They helped each other out throughout the game and it's a shame we didn't get all three points, but it was a balanced game.
"We always try to give our best in terms of performance and style, but at this moment in time it is more important to be solid, effective and allow few scoring opportunities to our opponents. If we do that, then we can build game by game.
"I have tried to teach courage, bring back some joy to the players and give them belief, which is perhaps more invisible than tactical changes. It is a crisis when a coach is fired, so I had to get the group back on track and in that sense I am satisfied with how we have progressed.
"The players are working very hard in training to improve and emerge from this situation. Tonight the result was another positive step forward."
Seedorf also swatted away suggestions that his job is on the line.
The recent poor run has resulted in crisis talks between Seedorf and the players with the club's fanatical Ultras, but the Milan coach insisted there has been no indications that he could lose his job.
"There was never a separation within the club," he told Sky Sport Italia.
"I was glad to see this reaction and character from the squad and club. In my press conference I also pointed out that I never received any of the indications from the president or CEO that I had a deadline or any of the other things written this week. I remain with the indications I received when I signed the contract.
"I am enjoying the experience, when it comes to the daily work, training and being with the players. I am growing every day."
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